MathDB

r=b+\frac{1}{a_1}+\frac{1}{a_2}+...+\frac{1}{a_n}

Source: Ukraine TST 2010 p12

May 5, 2020

algebrarationalSumreciprocal sumnumber theory

Problem Statement

Is there a positive integer

n

for which the following holds: for an arbitrary rational

r

there exists an integer

b

and non-zero integers

a _1, a_2, ..., a_n

such that

r=b+\frac{1}{a_1}+\frac{1}{a_2}+...+\frac{1}{a_n}